Ultraviolet-photoemission (UPS) measurements and supporting specific-heat, thermal-expansion, resistivity and magnetic-moment measurements are reported for the magnetic shape-memory alloy Ni$_2$MnGa over the temperature range $100K < T < 250K$. All measurements detect clear signatures of the premartensitic transition ($T_mathrm{PM}sim 247K$) and the martensitic transition ($T_mathrm{M} sim 196K$). Temperature-dependent UPS shows a dramatic depletion of states (pseudogap) at $T_mathrm{PM}$ located 0.3eV below the Fermi energy. First-principles electronic structure calculations show that the peak observed at 0.3eV in the UPS spectra for $T > T_mathrm{PM}$ is due to the Ni-d minority-spin electrons. Below $T_mathrm{M}$ this peak disappears, resulting in an enhanced density of states at energies around 0.8eV. This enhancement reflects Ni-d and Mn-d electronic contributions to the majority-spin density of states and is accompanied by significant reconstruction of the Fermi surface.